First slide
Planes in 3D
Question

The equation of a plane which passes through the point of intersection of lines x13=y21=z32 and x31=y12=z23 and at greatest distance from point (0, 0, 0) is

Moderate
Solution

Let a point (3λ+1,λ+2,2λ+3)  of the first line also lies on the second line. Then 

Hence, the point of intersection P of the two lines is (4, 3, 5).
Equation of plane perpendicular to OP, where O is (0, 0, 0), and passing through P is  4x+3y=5z=50

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